The coordinates of the vertex W are (5 , -1)
Step-by-step explanation:
In the parallelogram, the diagonal bisect each other
To find a missing vertex in a parallelogram do that:
- Find the mid-point of a diagonal whose endpoints are given
- Use this mid-point to find the missing vertex
- The mid point rule is
∵ WXYZ is a parallelogram
∴ Its diagonals are WY and XZ
∵ The diagonal bisect each other
- That mean they have the same mid-point
∴ They intersect each other at their mid-point
∵ x = (-2 , -3) and z = (7 , 7)
∴ = -2 and
= 7
∴ = -3 and
= 7
- Substitute them in the rule of the mid point to find the
mid-point of XZ
∴
∴ The mid-point of diagonals WY and XZ is (2.5 , 2)
Let us use it to find the coordinates of vertex W
∵ W = (x , y) and Y = (0 , 5)
∴ = x and
= 0
∴ = y and
= 5
- Equate 2.5 by the rule of the x-coordinate of the mid-point
∵
- Multiply both sides by 2
∴ 5 = x + 0
∴ 5 = x
∴ The x-coordinate of point W is 5
- Equate 2 by the rule of the y-coordinate of the mid-point
∵
- Multiply both sides by 2
∴ 4 = y + 5
- Subtract 5 from both sides
∴ -1 = y
∴ The y-coordinate of point W is -1
The coordinates of the vertex W are (5 , -1)
Learn more:
You can learn more about the mid-point in brainly.com/question/10480770
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